Risk in revenue management

Acknowledging risk’s existence and knowing how to minimize it.

By Param Singh

Most of us go about our daily actions in our personal lives constantly evaluating risk vs. reward elements. Most actions are based on decisions that are made quickly and sub-consciously with barely a thought regarding risk vs. reward, but others are more deliberate and calculating as, say, financial decisions to invest in the stock market.

We naturally carry our disposition regarding risk into the workplace, too, making on-the-job decisions based on our general attitude toward risk. People differ in the level of risk with which they are comfortable. So the question, then, is how does the variety in people’s willingness to take risk affect decisions that have an impact on the company’s bottom line?

Let’s narrow this question down to the world of revenue management (RM). RM systems help in the decision-making process by evaluating vast amounts of complex demand and supply information and recommending optimal actions to maximize revenues. But even so, RM analysts have a role, rightly so, in deciding whether or not to approve or adjust these system recommendations. But can they do that without imposing their viewpoint on risk into the equation?

Cruise line’s experiment evaluates effect of propensity to take risks

As a real-life example to understand this phenomenon, a revenue management department undertook an experiment with analysts using its RM system. This company was a cruise line so the resources being priced were cabins for future sailings of varying durations on ships with various itineraries. With several hundred sailings each year for this cruise line, the RM workload of the department was divided among its dozen analysts on the basis of the ship type, sailing duration, season and destinations.

The RM system evaluated the data and performed its modeling, forecasting and optimization steps to recommend prices for its products. The analysts either approved the system recommendations or adjusted the prices up or down.

The key metrics for evaluating individual sailings were occupancy and various flavors of net revenue. Revenue came from tickets for the cabins and cruise and onboard revenues from shopping, casinos, liquor, off-shore excursions, etc. High occupancy was desirable — sometimes at the cost of low ticket prices — for both the onboard revenue component plus the positive psychological effect on passengers (similar to customers feeling somewhat let down if the restaurant they went to dine in was sparsely occupied). Also, the cruise line preferred to raise ticket prices as the sail date approached, though this was not always upheld for various reasons such as poor forecasts, disbelief in forecasts or a variety of market conditions, giving rise to confusion from the customer’s point of view — some of whom thought it better to wait to get good deals on cruise prices.

As part of this experiment, a single small sample of future sailings of varying durations, itineraries, etc. was assigned to all RM analysts. This was workload over and above the individual collection of sailings they were each already responsible for. They were asked to evaluate the system recommendations for this handful of sailings and decide whether to accept it or assign new lower or higher prices. All analysts had the same data available to them. This experiment lasted several months since the sample consisted of sailings a few weeks from departure and others several months from departure. Even though only the “true owners” of the sample of sailings made the real implementable pricing decisions, all analysts recorded their pricing decisions and reasons behind them. This was done once a week, at the same frequency of the RM system forecasting/optimization runs, until the sailings departed.

The recorded results of decisions that would have been made had different RM analysts been in charge of these sailings were very informative. It became obvious that different people viewed the same information differently, sometimes to the point of making opposite decisions: If the system’s recommendation was to raise prices from their current level, some analysts suggested raising the price even higher whereas others suggested lowering the prices, the recommendations notwithstanding! And all this based on the same RM data elements.

The risk tolerance in its most extreme form was expressed by two divergent camps:

The pessimists. Analysts who would rather not wait till close-to-departure for higher revenue demand and filled the ship somewhat earlier by accepting demand sooner than later, thereby reducing the risk of empty cabins at sailing but also getting lower total revenues.

The optimists. Analysts who waited too long for the close-to-departure higher revenue demand and thus either suffered lower occupancy or did a last minute fire sale, resulting in lower total revenues.

One can debate which risk tolerance approach was best for the cruise line. The latter certainly sent the wrong message to the marketplace in terms of waiting for deals close to sailing, especially if it occurred often.

Another interesting observation was that senior management’s risk tolerance also played into the analyst decisions. Since all pricing decisions had to be approved by the managers and/or directors, their risk tolerance and preferences were superimposed upon each analyst’s decision-making process. In this case, a systemic shift of metrics occurred for the department as a whole during the time preceding the sailings: Early on, far from the sail date, the metric was net revenue (i.e., holdout and wait for higher valued demand), and, closer in as the sail date approached, the metric shifted toward occupancy.

Steps to minimize the effect of risk predispositions

Although it was reassuring that analysts did not blindly accept the RM system recommendations, it’s clear companies can better direct their efforts and minimize the risk-taking element through good RM models, training and metrics.

RM models. It’s vitally important to ensure the effectiveness of the five main pieces of your RM system:

Data: Good, clean and timely data in a single location provide a reliable foundation for downstream RM processes.

Estimation models: Accurate and frequently updated models provide the best supporting parameters used in the RM system. These include cancellation rates, segmentation, unconstraining and price elasticities.

Forecasting: Accurate prediction of demand as best as data will allow, and flexibility to incorporate new business conditions or information without delay.

Optimization: Good recommendations based on valid representations of the real world’s business constraints and market conditions, built to take advantage of advances from evolving mathematical techniques.

Tracking and reporting: Visibility into knowing that the models are working well and that optimal revenue opportunities are being captured.

Training. Training provides both an understanding and a belief in the RM system. Training underlines that RM models, if stochastic in nature, are generally risk neutral and on the average will provide superior revenue results compared to the “risk” taking by analysts which is akin to gambling. In the short term, it may pay off, but in the long term it will generate sub-optimal levels of revenues. If the analysts are trained to understand how the data is used, various parameters estimated, demand forecasted and optimization recommendations produced, they are more likely to know where to focus their efforts in determining the validity of the RM system decisions.

Metrics. Confidence in the recommendations produced by a RM system comes by producing and reviewing post-sailing metrics such as accuracy metrics of forecasts and other parameters used in the RM models and metrics of revenue opportunities captured. Showing analysts how well the forecasting models predict when the various demand streams can be expected to occur and did occur, will take them a long way in not unnecessarily second guessing the demand forecasts. And viewing revenue opportunity captured metrics (actual revenue captured on a scale of no RM revenue vs. optimal revenue possible) also shows them the direct results of RM actions, whether positive or negative in nature.

Risk sensitive models

Practitioners and researchers using RM in several industries have observed that risk averseness is a common and natural human behavior. That’s especially true as RM analysts make their decisions under the generally difficult condition where the higher revenue customers’ demand occurs toward the end of the booking cycle. That’s when compensating for poor RM decisions or sub-par models is most difficult.

Most of the mathematics used in the RM optimization models rely on both the long run — on the average, based on a high volume of flight departures, cruise sailings, hotel nights and car rentals — and therefore have risk-neutral revenue maximizing objective functions. But they don’t directly consider the fact that sometimes RM industries may prefer stable financial results in the short term rather than some of the inherent volatility produced with the use of risk-neutral models and market randomness.

Recent research and development of mathematical formulations incorporate a variety of mechanisms — called risk-sensitive formulations — into the RM models to mitigate these risk elements. Following are a number of different risk-sensitive methods incorporating a variety of levers to achieve an acceptable risk objective:

various utility functions as a way to reflect the level of risk that is acceptable;

variance of sales as a function of price by using weighted penalty functions;

value at risk or conditional value at risk functions;

relative revenue per available seat mile at risk metric, for airlines;

maximizing revenues, using constraints of minimum levels of revenue with associated probabilities; and

target percentile risk measures that prevent falling short of a revenue target.

(For more information and a comprehensive bibliography, see “Risk Minimizing Strategies for Revenue Management Problems with Target Values” by Matthias Koenig and Joern Meissner.)

Even though most current RM models are risk-neutral models, RM practitioners have to ensure that they do not make risk predisposition-based, sub-optimal decisions while trying to maximize revenues. If the RM models in use, whether forecasting or optimization, indeed are in need of risk adjustments, then those enhancements should be made. However, incremental benefits are possible from using good models to begin with, supported by frequent training and analytical review of results before incorporating additional risk-sensitive components into the RM models.

Param Singh, SAS Worldwide Marketing, has gained, over the past 15 years, a variety of cross-industry revenue management experience working in airlines, cruise lines, hotels and transportation. His responsibilities in RM have spanned all facets of revenue management systems including data management, forecasting, optimization, performance evaluation and metrics, reporting, GUI design, model calibration, testing and maintenance. Singh has also provided RM consulting services to several companies. Prior to RM, he worked in the application of a variety of operations research techniques and solutions in the airline industry in the areas of airport operations, food and beverage, maintenance and engineering.

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